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Given a sequence of values {a_k}_(k=1)^n, the high-water marks are the values at which the running maximum increases. For example, given a sequence (3,5,7,8,8,5,7,9,2,5) with ...

If every component L of X/O_(p^')(X) satisfies the "Schreler property," then L_(p^')(Y)<=L_(p^')(X) for every p-local subgroup Y of X, where L_(p^') is the p-layer.

You buy 100 pounds of potatoes and are told that they are 99% water. After leaving them outside, you discover that they are now 98% water. The weight of the dehydrated ...

Given a sequence of values {a_k}_(k=1)^n, the running maxima are the sequence of values {max(a_1,...,a_k)}_(k=1)^n. So, for example, given a sequence (3,5,7,8,8,5,7,9,2,5), ...

The partial differential equation partial/(partialx)(u_t+uu_x+1/2u_(xxx)+u/(2t))+(3alpha^2)/(2t^2)u_(yy)=0 which arises in the study of water waves.

A problem in the calculus of variations. Let a vessel traveling at constant speed c navigate on a body of water having surface velocity u = u(x,y) (1) v = v(x,y). (2) The ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

Consider a horse rider who wishes to feed his horse at a field, gather water from a river, and then return to his tent, all in the smallest overall distance possible. The ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

Given three jugs with x pints in the first, y in the second, and z in the third, obtain a desired amount in one of the vessels by completely filling up and/or emptying ...